The article is developed mathematical support of the component detection for useful stochasticperiodic radiosignals in telecommunication networks which based on the principles of the energy theory of stochastic signals applying the theory of periodically correlated random processes and component processing. On the basis of mathematical support is implemented algorithmic support for effective detection of useful stochastic-periodic radiosignals in telecommunication networks with interferences by calculating correlation components as quantitative indicators of detection. Mathematical and algorithmic support, detection, radiosignals, telecommunication network Ageeva D.V., Sosulina Y.G., Levina B.R., Gould B., Oppenheim A. and other notable scientists of the technical direction.
The problem of the process of efficient detection of useful radiosignals in telecommunication networks (computer networks, mobile networks, etc.) on the background of various types of interferences is the basic problem of radiosignal processing in the telecommunications industry. When solving the problems of processing radiosignals with interference, a number of works have a basic worth Ukraine
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Therefore, the development of new mathematical support, in particular the mathematical model of radiosignals and the implementation of new effective mathematical methods and algorithms for detecting useful radiosignals in telecommunication networks in the presence of interferences on its basis is an actual problem.
In the development of telecommunication networks (fig. 1), the transmission/reception channel is the basic link where the source of radio signals and blocks are coordinated.
The mathematical image of radiosignal network model of a real telecommunication network is directed for development of a mathematical apparatus of empirical radiosignals at the outputs/inputs of this telecommunication network and certain communication mechanisms of this network with the radiosignals of the network. For specify the indicators and characteristics of radiosignals in telecommunication networks, it is necessary to analyze the behavior of the values of real radiosignals, and on its basis to select the structure of the mathematical image of radiosignals.
Fig. 2 shows an amplitude-modulated radiosignal with the interferences in its structure.
Amplitude-modulated radiosignals in the telecommunications network are characterized by periodicity by the modulation method and stochasticity by the influence of interference of various natural and artificial origins.
Therefore, the mathematical image of the model should provide a constructive combination of periodicity and stochasticity. These needs are agreeing a mathematical image as a periodically correlated random process (PCRP), which organizes the process of ensuring the specified combination and has methods of processing radiosignals of the network for effective detection of the useful component in these radiosignals in telecommunication networks with interferences.
Because of the fact that the value of the power of radiosignals is limited and characterized by a
certain ending within one modulation period of time, it is possible to confirm that the radiosignal
belongs to the class known from the energy theory of stochastic signals (ETSS) as class T [
The radiosignals represent as the PCRP belong to the class T and represented in expression [
The selected representation of the mathematical image of the radiosignal by the PCRP model from the ETSS theory provides the development of means of detecting useful components in telecommunication networks with interferences based on in-phase or component processing by the calculation of numerical indicators of statistics as the correlation components.
The statistics of the correlation components in the component processing of the radiosignal are calculated according to the expression:
Bˆk u 1 T 0 0
t u t exp ik T 0 2
t dt , T 0 where t - centered implementation of the radiosignal relative to the average.
In fig. 3 sign operations: 1 – calculation of the average statistics of the radiosignal m t ; 2 – modeling of a consistency of average radiosignal statistics [ m t m t m t … m t ] by their periodic arrangement; 3 – a procedure for centering a radiosignal relative to a set of consistency average statistics t ; 4 – the procedure for calculating radiosignal components Bk u ; 5 – the procedure for evaluating radiosignal components Bk u as indicators of their detection in a network with interferences Y k ; 6 – procedure for making decisions about the presence of a useful radiosignal.
The result of calculating the correlation components of the radio signal of the network with the existing interference component with the dispersion 0 мВ2 (without interference) is shown in fig. 4.
(а) (b) Figure 4: The result of detection of a network radiosignal with an interference component with a dispersion 0 mV2 (abscissa axis – shift, ordinate axis – component number, applied axis power (mV2)): а) radiosignal; b) components as a result of detection
On fig. 4, it can be seen that the components of the useful radio signal (fig. 4, a) are clearly localized according to the correlation components as a detection indicator (fig. 4, b).
The result of calculating the radiosignal components of the network with an existing interference component with a dispersion 1 мВ2 is shown in fig.5.
The averaged components (fig. 6) provide a more detailed comparison procedure when compared with non-averaged components (fig. 4-5, a), which guarantees the effective detection of radiosignals in telecommunication networks with interferences.
According to the results of processing radiosignals, in particular their averaged components of the radiosignal with interference, it was established that the developed mathematical and algorithmic support is provides the process of detecting and tracking the presence of useful radiosignals in telecommunication networks with the given distortions. Such facts indicate the effectiveness of the radiosignal detection procedure which based on the developed mathematical and algorithmic support.